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MA100 (2)

# 100wk12solnsf13.pdf

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School
Wilfrid Laurier University
Department
Mathematics
Course
MA100
Professor
Christine Zaza
Semester
Fall

Description
MA100 Week 12 Report - Graphing Name: Student Number: Lab Fall 2013 1. [4 marks] Suppose f(x) = x + 5x . Determine the absolute maximum and the absolute minimum of f for x 2 [▯2;2]. f (x) = 0 () 5x + 20x = 0 Now: f(▯2) = ▯32 + 5(16) = 48 () 5x (x + 4) = 0 f(0) = 0 ! absolute minimum () x = 0 since x = ▯4 2= [▯2;2] f(2) = 32 + 5(16) = 112 ! absolute maximum ex 2. [22 marks] Consider the function f(x) = : x + 1 (a) State the domain of f using interval notation. dom f (▯1;▯1) [ (▯1;1) (b) Determine any x-intercepts and y-intercepts of f. y-int ) f(0) = 1. There is a y-int at (0;1). There are no x-int as f(x) 6= 0. (c) Consider lim f(x) and lim f(x) and comment on the vertical asymptotes of f. x!▯1 + x!▯1▯ ex ex lim▯ f(x) = lim ▯ lim+ f(x) = lim+ x!▯1 x!▯1 x + 1 x!▯1 x!▯1 x + 1 ▯1 ▯1 e e + = +1 ▯ = ▯1 0 0 ) There is a vertical asymptote at x = ▯1 e ex (d) Given that lim = 1 and lim = 0, ▯nd all horizontal asymptotes of f (if any). Justify your x!1 x x!▯1 x answer. x x lim f(x) = lim e lim f(x) = lim e x!1 x!1 x + 1 x!▯1 x!▯1 x + 1 ex ▯ ▯ ex ▯ ▯ = lim x approaches 1 = lim x approaches 0 x!1 1 + 1 1 x!▯1 1 + 1 1 x x = 1 = 0 ) y = 0 is the only H.A. x x▯ 2 ▯ (e) Show that f (x) = xe an
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